2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104833For a ringed space (X,O), we show that the deformations of the abelian category Mod(O) of sheaves of O-modules are obtained from algebroid prestacks, as introduced by Kontsevich. In case X is a quasi-compact separated scheme the same is true for Qch(O), the category of quasi-coherent sheaves on X. It follows in particular that there is a deformation equivalence between Mod(O) and Qch(O).29 pagesAlgebraic Geometry18E15; 18F20text